The Relative Efficiency of Regression and Simple Unit Predictor Weights in Applied Differential Psychology

A very common problem in the behavioral and social sciences is the prediction of the standing of a person or thing on one variable, usually designated the criterion, from his or its standing on a number of other variables, usually called the predictors. Leastsquared error multiple regression weights are most commonly used in weighting the predictors into a composite. These weights, which minimize, over the cases in the sample, the sum of the squared deviations of the observed from the predicted criterion score, are calculated from the normal equations which express the minimization conditions (Anderson, 1958). The fitting of the regression weights to the idiosyncracies of the initial sample leads to a decrease in effectiveness when these weights are applied to a new sample in which these particular idiosyncracies are not present. This &dquo;shrinkage&dquo; is often substantial in practical situations (e.g., see: Kurtz, 1948; Cureton, 1950; and Kirkpatrick, 1951), especially when the initial sample is small. And small samples, as Lawshe and Schucker (1959) point out, are the rule rather than the exception in many areas of applied psychology. Certain other approaches to the weighting problem produce